Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 5 - Section 5.1 - Proving Identities - 5.1 Problem Set - Page 279: 17

Answer

As left side transforms into right side, hence given identity- $\frac{\tan A}{\sec A}$ = $\sin A$ is true.

Work Step by Step

Given identity is- $\frac{\tan A}{\sec A}$ = $\sin A$ Taking L.S. $\frac{\tan A}{\sec A}$ = $\frac{\sin A/\cos A}{1/\cos A}$ ( Using reciprocal and ratio identities) = $\frac{\sin A}{\cos A} . \frac{\cos A}{1}$ = $\sin A$ = R.S. As left side transforms into right side, hence given identity- $\frac{\tan A}{\sec A}$ = $\sin A$ is true.
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